1. Field of the Invention
The present invention relates to a method to determine quantity, distribution, and speed of recovery of hydrocarbons in oil and gas subterranean reservoirs. More particularly, the present invention is a method for using petrophysical data from a plurality of wells, in a plurality of reservoir regions, containing a plurality of reservoir rock types, in the context of a three dimensional geological model, for identifying dimensionless capillary pressure functions (DCPF) and using these dimensionless capillary pressure functions for determining reservoir fluid volumes, fluid contacts, the extent of reservoir compartmentalization, and an improved estimate of reservoir permeability.
Aspects of the present invention draw from the fields of geology, geophysics, petrophysics, petroleum engineering, and applied mathematics. The present invention relates to methods for assisting engineers, geologists, and others to address the following key issues in the development of oil and gas reservoirs: the calculation of the distribution and volume of hydrocarbons in place, the degree to which reservoir fluids are contained in isolated flow compartments, and the speed with which fluids may be recovered. The first issue concerns the concepts of porosity and fluid saturations, which are, respectively, the fraction of the rock volume available for reservoir fluids and the fraction of the pore space containing a particular fluid. The second issue concerns the concept of reservoir compartmentalization, the degree to which reservoir fluids flow in isolated flow units. The third issue concerns the concept of permeability, a parameter that relates fluid flow rates to imposed pressure gradients, which can be due to injection of fluids or to natural conditions such as aquifers or gas caps. The present invention relates to a method for using dimensionless capillary pressure functions as derived from well logs to calculate saturations and fluid contacts, identify reservoir compartments, and improve on estimates of permeability in three-dimensional geological models.
2. Prior Art.
In general, the present invention is a method for assisting engineers, geologists, and others associated with the development of oil and gas subterranean reservoirs to address questions concerning how much hydrocarbons are in a given location, how they are distributed within that location, and how fast can they be recovered from this given location. The present invention helps to address all three of these questions whereas the prior art has known disadvantages.
It is well known that reservoir fluids are distributed according to the interplay of gravitational and capillary forces. Capillary pressure curves, which describe capillary forces, are typically measured in laboratory experiments. In one such type of an experiment, a completely water-saturated rock is exposed to oil. Typically, in the case of water-wet rock, oil does not enter the pore space of the rock until a certain pressure, referred to as the displacement pressure or entry pressure, is exceeded. As the oil pressure is increased above the entry pressure, more and more oil enters the pore space and a corresponding amount of water leaves the pore space. As pressure continues to increase, it becomes increasingly difficult to remove water: there is proportionately less and less water leaving the rock. Eventually, at high oil pressures, a low saturation of water remains. This water saturation is referred to as the irreducible water saturation. The shape of the capillary pressure curve is an indicator of the distribution of the sizes of the pores within the porous media. Thus, rocks of various porosities and permeabilities exhibit widely varying capillary pressure curves. Thus, capillary pressure curves are used to characterize reservoir rocks.
Reservoirs contain various compositions of oil, water, and gas that are distributed within heterogeneous rocks, exhibiting a high degree of variability in porosity and permeability. For example, if the reservoir were deposited within a fluvial (relating to ancient rivers or channels) environment, there is typically a high degree of heterogeneity, both in an inter-channel and intra-channel areas. On the larger, inter-channel scale, the channels would exhibit high permeabilities; whereas, intervening flood plain deposits would be of lower permeabilities, and intervening shales would exhibit little or no permeability. On the intra-channel scale, one might encounter highly heterogeneous porosities and permeabilities in mud clast rocks at the base of a channel (where the ancient rates of sediment transport were highest). Higher up in a given channel, one might encounter plane and cross-bedded rocks exhibiting high permeabilities. These might grade up into finely sorted ripple laminated facies exhibiting uniform, but lower, permeabilities. Heterogeneous reservoirs, whether they are comprised of sandstones, carbonates, or other types of rocks are the norm.
In general, two rock samples from the same reservoir will have different capillary pressure curves when their permeabilities and/or porosities are different. Consequently, given the typical high degree of reservoir heterogeneity, a representative characterization of reservoirs using capillary pressure curves is likely to be an arduous task. Complex geological models containing in excess of a million cells can, in principle, require millions of measurements to describe the necessary capillary pressure curves.
More than fifty years ago, Leverett identified a way around this problem by proposing a dimensionless capillary pressure curve called the J Function,
      J    ⁡          (              S        w            )        =                    P        c            ⁢                        k          ⁢                                  ϕ                                      σ      ⁢                          ⁢      cos      ⁢                          ⁢      θ      See Leverett, M.C., “Capillary Behavior in Porous Solids”, Transactions of the AIME 142, 152–169 (1941). In this equation, Sw denotes water saturation; Pc, capillary pressure; k, permeability; φ, porosity; σ, interfacial tension; and θ, contact angle. Upon analyzing experimental data, Leverett discovered that many rock samples, within a certain rock type or classification, exhibited one characteristic curve instead of multiple capillary pressure curves. Thus, the advantage of his approach is that many rock samples exhibiting various porosities and permeabilities are, within a particular rock type, classifiable by a single curve. Consequently, the problem of describing millions of capillary pressure curves for a geological model can be reduced to using a manageable number of Leverett J Functions. Typically, Leverett J Functions are correlated with parameters such as lithology, shale volume, and reservoir zone.
The present invention generalizes the equation of the Leverett J Function into a function that is, heretofore, referred to as the dimensionless capillary pressure function. It is defined as follows:
      J    ⁡          (              S        w            )        =                              P          c                ⁢                  k                            σ        ⁢                                  ⁢        cos        ⁢                                  ⁢        θ              ⁢          f      ⁡              (        ϕ        )            
Like Leverett's J Function, this new function is dimensionless. In this equation, f denotes a function of porosity, thus generalizing the dependence on porosity and reducing to Leverett's result when the function f is the reciprocal of the square root. Leverett defined the function as φ−n where n=½ as is depicted in the previous formula. It is contemplated that the variable n may be any other positive number as depicted.
There are known expensive and time consuming methods which attempt to determine aspects of subterranean formations for evaluation of oil and gas recovery with various application identifying dimensionless capillary pressure functions from laboratory measurements on core samples. The latter refers to small segments of reservoir rock that are recovered from wells. Oftentimes, due to the additional costs of coring operations, core samples are not recovered from many oil and gas wells. Typically, when they are recovered, they represent a sparse sampling of reservoir rocks within a well. Consequently, dimensionless capillary pressure functions obtained from laboratory measurements on core samples may poorly represent the heterogeneity of the reservoirs of interest. The present invention determines dimensionless capillary pressure functions from well logs. Consequently, in comparison to laboratory determinations, the present invention more broadly samples reservoir heterogeneities, as exhibited in wells. Moreover, the present invention places such information gained at the wells in context with a geological model of reservoir and fluid properties, thus leading to its more effective use in calculating the distribution and volume of hydrocarbons in place, the degree to which reservoir fluids are contained in isolated flow compartments, and the speed with which fluids may be recovered.
Throughout the oil and gas industry, computer models of reservoir and fluid properties are used to assess the amounts and distributions of recoverable hydrocarbons and to forecast their production. Increasingly, integrated, interdisciplinary teams of geologists, petrophysicists, petroleum engineers, geophysicists, and other reservoir scientists and engineers construct such computer models. In fact, these models are often used as repositories of diverse and heterogeneous types of reservoir data that are acquired by the various members of the team.
Typically, these models contain measured data from borehole or surface geophysical measurements. Borehole measurements are of high resolution (less than one foot) but pertain to a very limited portion of the entire model, thus leaving the interdisciplinary team to grapple with issues of how properly to interpolate or distribute borehole measurements into the full expanse of the interwell region within the three-dimensional model. Surface measurements sample a far larger portion of the model than boreholes, but at far lower resolution (up to hundreds of feet), thus providing the team with only limited guidance on the issue of interpolating or distributing properties from the boreholes.
In recent years, great attention and many technical papers have focused on the issues of building such models and of distributing various properties within them. Typically, these methods entail distributing properties such as lithology, porosity, permeability, seismic impedance, etc. Such methods tend to focus on the sensible distribution of properties with reference to a geostatistical or geological (both structural and stratigraphic) framework. Notably absent from these methods is a method for the systematic and rigorous distribution of fluid saturation information from well logs into the three-dimensional region between wells. As opposed to other reservoir properties, fluid saturations are not merely dependent on the geostatistical or geological frameworks but must conform to well-understood principles of capillarity, which govern their distributions with regards to, say, porosity and permeability. The present method honors (indeed can reproduce exactly) all saturation data within wells while distributing saturations between wells according to well-established principles of capillarity.
A number of prior-art patents address the issues of geological modeling, in general, and the geostatistical distribution of properties within a model. U.S. Pat. No. 4,646,240, entitled METHOD AND APPARATUS FOR DETERMINING GEOLOGICAL FACIES issued to Serra et al., describes a technique for automatically determining lithological facies from well-log data.
U.S. Pat. No. 4,991,095, entitled PROCESS FOR THREE-DIMENSIONAL MATHEMATICAL MODELING OF UNDERGROUND VOLUMES issued to Swanson, describes a technique for subsurface modeling utilizing a regular grid in the longitude-latitude plane and arbitrary resolution in the depth direction.
U.S. Pat. No. 5,416,750, entitled BAYESIAN SEQUENTIAL INDICATOR SIMULATION OF LITHOLOGY FROM SEISMIC DATA issued to Doyen et al., describes a geostatistical method for distributing lithology data into a three-dimensional geological model.
U.S. Pat. No. 5,995,906, entitled METHOD FOR RECONCILING DATA AT SEISMIC AND WELL-LOG SCALES IN 3-D EARTH MODELING issued to Doyen et al. describes a geostatistical method for reconciling the disparity in scale between vertically detailed log measurements of a selected rock property in boreholes and vertically-averaged measurements of the same rock property as derived from seismic observations over a region of interest.
U.S. Pat. No. 6,044,328, entitled METHOD FOR CREATING, TESTING, AND MODIFYING GEOLOGICAL SUBSURFACE MODELS issued to Murphy et al., describes a computer-implemented method for managing geological hypotheses and constructing geological models with reference to a known archive of geological structures.
On the one hand, prior-art methods for distributing properties between wells prove inappropriate for calculating fluid saturations because of inattention to principles of capillarity. On the other hand, prior-art methods for interpreting well log data to determine, say, formation boundaries, oil-water contacts, or hydraulic flow units rely on a restrictive set of equations and/or provide no methodology for distributing saturations into the three-dimensional model while honoring well log data. Moreover, prior-art methods for interpreting well log data tend not to incorporate geological information that has, through the above-mentioned geological modeling methods, been distributed within the three-dimensional geological model. In counter distinction, the present method uses information such as reservoir zone, fault block, lithology, etc. (that are usually found in three-dimensional reservoir geological models) to aid the interpretation of well log data.
A number of prior-art patents address the issues of determining formation boundaries, flow units, or oil-water contacts from well log data. U.S. Pat. No. 4,648,268, entitled METHOD OF DEFINING HOMOGENEOUS ROCK FORMATION ZONES ALONG A BOREHOLE ON THE BASIS OF LOGS issued to Grosjean, describes a method for processing well-log data to define formation boundaries along the borehole.
U.S. Pat. No. 5,193,059, entitled METHOD FOR IDENTIFYING AND CHARACTERIZING HYDRAULIC UNITS OF SATURATED POROUS MEDIA: TRI-KAPPA ZONING PROCESS issued to Tiab et al., describes a method for defining formation units of similar hydraulic characteristics by means of core measurements and for relating the hydraulic characteristics of such units to macroscopic measurements of the formation as provided by wireline logs.
U.S. Pat. No. 5,621,169, entitled METHOD FOR DETERMINING HYDROCARBON/WATER CONTACT LEVEL FOR OIL AND GAS WELLS issued to Harris et al., describes a method for predicting the hydrocarbon/water contact level for oil and gas wells that relates porosity, water saturation, air permeability, and capillary pressure. The method relies on a worldwide correlation of permeability and porosity to a function of capillary pressure.
None of the prior-art approaches, either individually or collectively, address the need for a method for distributing saturations into a three-dimensional geological model whereby the saturation distribution honors both well-established principles of capillarity as well as the measured saturations within boreholes. The present invention, as described below, addresses these and other needs.